Killer sudoku combinations

Killer sudoku also killer su dokusumdokusum dokusumokuaddokuor samunamupure is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, killer sudoku combinations, depending on the solver's skill at mental arithmetic ; the hardest ones, however, can take hours to solve. A typical problem is shown on the right, using colors to define killer sudoku combinations groups of cells. More often, puzzles are printed in black and white, with thin dotted lines used to outline the "cages" see below for terminology.

Killer Sudoku adds a new dimension to standard Sudoku, requiring arithmetic to solve. You will need new specialised Killer Sudoku solving techniques to progress in these puzzles besides the standard Sudoku techniques you will already know. An essential Killer Sudoku solving technique is the "45 rule". This uses the fact that every row, column and block must contain each of the numbers 1 to 9 once. Therefore, the total of all numbers in one row, column or block will always be Take the first column of the Killer Sudoku shown in Figure 1. The numbers in this column will add up to

Killer sudoku combinations

Remembering common unique combinations is essential if you want to improve your time for solving killer sudoku puzzles. As well as cell cage combinations, we've included required digits further down. Some cells always require particular digits, regardless of the number combination that goes into them. Knowing these is a great way to eliminate candidate numbers from blocks, rows, and columns. Is it cheating? We call it a cheat sheet, but is it really cheating? Only you can decide! Our view is that a reference like this is no more cheating than using a dictionary to check your spelling. For us, puzzles like killer sudoku are all about the logic and not an exercise in memory or recall. New to killer sudoku? Be sure to check out our Killer Sudoku From Scratch tutorial. Love logic puzzles? Be sure to check out Puzzle Weekly — our free weekly collection, delivered to your inbox every Monday. Click here to find out more, and to get your free subscription. These are all possible combinations of digits for a given cage size and sum.

Adding together a number ending in 7 and a number ending in 8 always results in a number ending in 5, for example.

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Table of Contents Introduction Basic Solving Stragegies Example basic puzzle More advanced example based on weekly 24 More advanced example based on weekly 28 More advanced example based on weekly 74 A daily is easier than it looks More advanced example based on weekly Killer Sudoku Solving Strategies There are three basic methods used to solving killer sudoku puzzles. The first is to use the strategies for solving regular sudoku puzzles. The second is to consider the different ways that a sum can be created. The third is to consider the total value of a region. Here we outline the basic strategies and then show how they are applied in a sample puzzle.

Killer sudoku combinations

Killer Sudoku is a variation that adds additional sub-regions of 2 or more cells with a number in the corner of each sub-region. The numbers placed in the cells of the sub-region must be unique in that sub-region even it the sub-region spans more than one row, column or region and must add up to the number in the corner of the sub-region. Sub-regions are shown by dotted lines which group cells together. You can use all the standard Sudoku Solving Techniques with Killer Sudoku, but there are several techniques specific to the addition of the sub-regions. The Rule of 45 is a key technique that can be extended to multiples of 45, along with Combination Elimination. These are explained below. The Rule of 45 can lead you to some simple placements as you begin to solve. If all sub-regions but one are fully contained in a row, column or region inside cells its possible to work out the value of the remaining cells outside cells.

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As a 2-cell cage totalling 4 can contain only 1 and 3, we deduce that a 7-cell cage totalling 41 contains neither 1 nor 3. Learn how and when to remove these template messages. The numbers in this column will add up to Please help improve this article by adding citations to reliable sources. Even though, initially, there is no way to tell which combination of numbers is correct, every solution available has a 1 in it. This does not seem particularly useful, but consider that the cell in the bottom right of the nonet is part of a 3-cage of 6; it can therefore only contain 1, 2 or 3. Download as PDF Printable version. The 14 cage can now be completed by solving the other square as a 9. These are all possible combinations of digits for a given cage size and sum. A short-cut to calculating or checking the value of a single 'innie' or 'outie' on a large number of cages is to add up the cages using 'clock' arithmetic formally, Modular Arithmetic modulo 10 , in which all digits other than the last in any number are ignored. This article needs additional citations for verification. When two numbers are added together, the last digit of the total is not affected by anything other than the last digits of the two original numbers.

Remembering common unique combinations is essential if you want to improve your time for solving killer sudoku puzzles. As well as cell cage combinations, we've included required digits further down.

By adding up the cages and single numbers in a particular house, the user can deduce the result of a single cell. The objective is to fill the grid with numbers from 1 to 9 in a way that the following conditions are met:. As a 2-cell cage totalling 4 can contain only 1 and 3, we deduce that a 7-cell cage totalling 41 contains neither 1 nor 3. Arithmetical puzzle game. For us, puzzles like killer sudoku are all about the logic and not an exercise in memory or recall. Be sure to check out Puzzle Weekly — our free weekly collection, delivered to your inbox every Monday. This article includes a list of general references , but it lacks sufficient corresponding inline citations. Call this the 'inside total', because it is the total of all cages which lie completely inside the column. The biggest number an 'innie' or 'outie' can hold is 9, so adding or subtracting that value will change the last digit of the total in a way that no other value would - allowing the 'innie' or 'outie' to be directly calculated. Love logic puzzles? This could also have been solved another way, by finding the 'outside' total - the total of all cages within the column, including the one lying partly outside. They then know that the 1 can only reside in cells that are outside of this nonet.